A substance `A_(x)B_(y)` crystallises in a face centred cubic (fcc) lattice in which atoms 'A' occupy each corner of the cube and atoms 'B' occupy face centered position of the cube. If five of the B atoms are missing from five face center, identify the correct formula of the compound.

Options

A. `AB_(3)`
B. `A_(4)B_(3)`
C. `A_(2)B`
D. Formula cannot be specified

Explanation

To determine the correct formula of the compound \( A_xB_y \) that crystallizes in a face-centered cubic (fcc) lattice with specific arrangements of atoms, we can follow these steps:

### Step 1: Analyze the fcc lattice structure
In a face-centered cubic lattice:
- There are 8 corner atoms.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.
- There are 6 face-centered positions, and each face-centered atom contributes \( \frac{1}{2} \) of an atom to the unit cell.

### Step 2: Calculate the contribution of atom A
Since atom A occupies each corner:
- Total contribution from corner atoms = \( 8 \times \frac{1}{8} = 1 \) atom of A.

### Step 3: Calculate the contribution of atom B
Atom B occupies the face-centered positions, but we need to account for the missing atoms:
- Normally, if all face-centered positions were occupied, the contribution would be \( 6 \times \frac{1}{2} = 3 \) atoms of B.
- However, since 5 of the B atoms are missing, only 1 face-centered atom remains.
- Therefore, the contribution from B = \( 1 \times \frac{1}{2} = \frac{1}{2} \) atom of B.

### Step 4: Write the ratio of A to B
Now we have:
- 1 atom of A
- \( \frac{1}{2} \) atom of B

The ratio of A to B can be expressed as:
\[ A : B = 1 : \frac{1}{2} \]

### Step 5: Convert the ratio to whole numbers
To convert the ratio \( 1 : \frac{1}{2} \) into whole numbers, we can multiply both sides by 2:
\[ 1 \times 2 : \frac{1}{2} \times 2 = 2 : 1 \]

### Step 6: Write the final formula
Thus, the formula of the compound can be written as:
\[ A_2B \]

### Conclusion
The correct formula of the compound is \( A_2B \).